Optical Materials. Optimizing refractive index and dispersion

Transcription

1 Optical Materials General comments Specifying optical materials Dispersion Thermal coefficients Athermalization Thermal expansion Thermal variation of refractive index Other glass data Optimizing refractive index and dispersion Model glasses Fixing glasses Axial and lateral chromatic aberration Calculation of chromatic aberration February 001 Optical System Design (week 4) 1

2 General comments Selection of optical materials Spectral region environment Application In refracting system Predominant material is glass However, like lens, glass may refer to a wide variety of materials Key issue Dispersion (may cause chromatic aberration) February 001 Optical System Design (week 4)

3 Some introduction Every optical systems works in its own particular wavelength region determined by the spectral characteristics of the light source, the spectral sensitivity of the sensor, as well as any other factors or components which alter the net sensitivity of the system. Photopic spectral eye sensitivity curve If an optical system is a visual system, February 001 Optical System Design (week 4) 3

4 Overview February 001 Optical System Design (week 4) 4

5 Specifying optical materials Dispersion Thermal characteristics Weight Mechanical Chemical Availability cost February 001 Optical System Design (week 4) 5

6 February 001 Optical System Design (week 4) 6 dispersion Sellmeier formula ) ( c b c b c b n = (wavelength unit: um) Adopted by Schott and other glass manufacturers

7 February 001 Optical System Design (week 4) 7 Formally, optical glasses were usually described by a Laurent series ) ( A A A A A A n = Conrady s simplified formula ) ( B A n n + + =

8 Buchdahl s chromatic coordinate for accurately characterizing the refractive index Chromatic coordinate ω() ω ( ) = 1+.5( 0 Reference wavelength Helium d line ( um) 0 ) n( ω ) + v + v + v = n ω ω ω... Index of refraction at d line February 001 Optical System Design (week 4) 8

9 Homework 4-1 Find out the following two papers and make a short brief (summary) P. N. Robb and R. I. Mercado Calculation of refractive indices using Buchdahl s chromatic coordinate, Appl. Opt., (1983) G. W. Forbes, Chromatic coordinates in aberration theory, J. Opt. Soc. Amer. 1, (1984). February 001 Optical System Design (week 4) 9

10 How to describe the dispersion of optical glass Abbe number (V number) V = n d 1 n n F c Index of refraction at the Helium d line ( um) Index of refraction at the hydrogen F ( um) Index of refraction at the hydrogen C line ( um) February 001 Optical System Design (week 4) 10

11 How to describe the dispersion of optical glass Dispersion: the difference in the refraction of indices for two wavelength Principal dispersion: the wavelengths are the F and C lines Partial dispersion: for other lines and usually expressed as a ratio, e.g., the relative partial dispersion for the F and d lines is P F, d February 001 Optical System Design (week 4) 11 n = F n F n n d c

12 Typical glass map February 001 Optical System Design (week 4) 1

13 Glass Map ( less dispersive) February 001 Optical System Design (week 4) 13

14 Crown and flint Crown N d > 1.6, V d > 50 or N d < 1.6, V d > 55 Flint The others Available refractive indices range from 1.45 to and the V number from 80 to 0 February 001 Optical System Design (week 4) 14

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16 Focusing of white light with an achromatic doublet from BK7 and SF glasses Let us consider two thin lens as shown in the right We want to find the condition for this doublet to be an achromatic doublet, chromatically corrected for the red C line wavelength (656.7 nm) and for the blue F line ( nm) The central wavelength is usually chosen as the d line nm Slightly defocusing toward the lens February 001 Optical System Design (week 4) 16

17 February 001 Optical System Design (week 4) 17 The power of first lens P 1, the second lens P (for d line) The total power P=P 1 +P An achromatic doublet will have the same power for the C line wavelength and the F line wavelength if (P 1 +P ) c =(P 1 +P ) F = d F c d F c n n n P n n n P n F n c V = 1 n d Abbe number: V V V V f f V V f f = = 1 1 P V V P =

18 Thermal coefficient In OSLO tem 40 (set temperature of lens to 40 degree C) pre 0.9 (set the pressure to 0.9 atmosphere) tce 5 18 (set surface 5 thermal expansion to 18X10-7 ) L( T + T ) = (1 + α T ) L( T ) Expansion coefficient February 001 Optical System Design (week 4) 18

19 (aluminum) spacer February 001 Optical System Design (week 4) 19

20 Strehl ratio: The ratio of peak value of the point spread function to the peak of the PSF for an equivalent (unaberrated) system. February 001 Optical System Design (week 4) 0

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23 Autofocusing (add one more compensator) February 001 Optical System Design (week 4) 3

24 Other glass data February 001 Optical System Design (week 4) 4

25 Optimizing refractive index and It is not easy to optimize the glass in the optical system since the index and dispersion can not be varied. For optimization calculation, we need to have a continuous model. To solve this problem, some approaches was used in OSLO Otherwise, OSLO can search all lenses in the catalog to get the closet glass (RMS distance) dispersion V number February 001 Optical System Design (week 4) 5

26 In optimization, we need Normal glasses Partial dispersion at any wavelength is proportional to the V number nx ny Pxy axy + b n n F c xy V February 001 Optical System Design (week 4) 6

27 Axial and lateral chromatic Two types of chromatic aberration First order, paraxial color Axial color PAC (primary axial color) Lateral color PLC The red and blue focus have been made to coincide, but the effective focal length of lens is different different magnification will be different aberration February 001 Optical System Design (week 4) 7

28 Calculation of chromatic aberration February 001 Optical System Design (week 4) 8

29 Some other terms Secondary spectrum The design of achromatic doublet is for F and C lines Depends on the choice of glasses, there will be a residual mismatch of dispersions, resulting in a larger or smaller secondary spectrum Secondary axial color (SAC) Secondary lateral Color (SLC) Spherpchromatism Change in spherical aberration with wavelength February 001 Optical System Design (week 4) 9

30 Parametric Examples of Glass Selection (1) (Both are normal glasses) (anomalous dispersion/normal glass) (anomalous/normal) (anomalous/anomalous) Secondary spectrum correction as a function of glass selection February 001 Optical System Design (week 4) 30

31 Homework 4- Please use OSLO LT and take a simple doublet to simulate above four cases, i.e., secondary spectrum correction by glass selection. February 001 Optical System Design (week 4) 31

32 Parametric Examples of Glass Selection () Spherical aberration and secondary spectrum correction as a function of f/# February 001 Optical System Design (week 4) 3

33 Parametric Examples of Glass Selection (3) Spherical aberration and secondary spectrum correction as a function of f/# February 001 Optical System Design (week 4) 33

34 Parametric Examples of Glass Selection (4) Secondary spectrum correction as a function of glass selection with one aspheric surface February 001 Optical System Design (week 4) 34

35 Plastic Optical Material Low-cost materials Low-cost fabrication techniques Configuration flexibility A common use Glass-plastic mixed system Plastic was used as Aspherical corrector Save money February 001 Optical System Design (week 4) 35

36 Types of Plastic optical material Acrylic ( ; ) Most common and important Good clarity and very good transmission in visible spectrum, high Abbe number, good machine stability Easy to machine and polish Good material for injection molding February 001 Optical System Design (week 4) 36

37 Types of Plastic optical material Polystyrene ( ) Good plastic, cheaper than acrylic Slightly higher absorption in the deep blue spectrum Index of refraction is higher than that of acrylic but with a lower Abbe number Lower resistance to UV and scratches that acrylic Acrylic and polystyrene make a viable achromatic pair February 001 Optical System Design (week 4) 37

38 Types of Plastic optical material Polycarbonate Expensive than acrylic High impact strength Very good performance over a broad temperature range Often used as plastic eyeglass Common form: CR39 February 001 Optical System Design (week 4) 38

39 Types of Plastic optical material COC (Zeonex) Similar to acrylic, but water absorption is much lower and higher heat distortion temperature (HDT) brittle February 001 Optical System Design (week 4) 39

40 Optical and physical properties of optical plastic February 001 Optical System Design (week 4) 40